2013/10/24 by Piotr Kokocki, Kokocki, Piotr
Computer Science · Engineering · Mathematics · #35L10 #35P05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1310.6794
openalex publication_date 2013/10/24 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We are interested in the differential equation u(t) = -A u(t) - c A\n u(t) + \λ u(t) + F(t,u(t)), where c > 0 is a damping factor, A\nis a sectorial operator and F is a continuous map. We consider the situation\nwhere the equation is at resonance at infinity, which means that \λ is\nan eigenvalue of A and F is a bounded map. We introduce new geometrical\nconditions for the nonlinearity F and use topological degree methods to find\nT-periodic solutions for this equation as fixed points of Poincar 'e\noperator.\n